Relativistic magnetohydrodynamics from kinetic theory

Abstract

This thesis develops a kinetic-theory framework for relativistic dissipative magnetohydrodynamics under strong electromagnetic fields, motivated by quark-gluon plasma in heavy-ion collisions. Starting from the relativistic Boltzmann-Vlasov equation and using the method of moments within the 14-moment approximation, it derives causal second-order hydrodynamic equations for relativistic plasmas with increasing generality. The work first review relativistic dissipative hydrodynamics and its kinetic foundations, emphasizing the need for Israel-Stewart-type transient theories to preserve causality and stability. Electromagnetic fields are then introduced at the microscopic level, where the Lorentz force modifies the moment hierarchy and produces anisotropic transport effects absent in field-free fluids. Next, it develops relativistic dissipative magnetohydrodynamics for a non-resistive two-component plasma of oppositely charged particles. Here, the magnetic field couples the dissipative sectors of the two species, generating relative dissipative currents and coupled shear dynamics. For Bjorken expansion, the theory predicts damped oscillations in the transverse shear sector associated with cyclotron motion. Finally, the thesis treats the resistive two-component case, where the electric field evolves dynamically and couples to charge diffusion and shear stress. The resulting theory reveals current-shear feedback, transient electromagnetic generation of momentum anisotropy, and underdamped dissipative oscillations. Applications to homogeneous and Bjorken-expanding plasmas show how resistive and electromagnetic effects modify evolution beyond standard hydrodynamics. Overall, the thesis extends relativistic dissipative hydrodynamics to magnetized and resistive plasmas, providing a microscopic foundation for future studies of strongly magnetized quark-gluon plasma and astrophysical systems.